Yes, I followed the ones posted. None of them say the opposite, they all leave out the results from the lidded flushes. And someone else posted a paper that showed that although lid closed produced fewer particles, they were larger, and lasted longer, so flushing lid closed was not particularly more hygienic.
Although Mythbusters is not a peer reviewed scientific source, they do employ reasonable standards of experimentation.
And the first source you posted is particularly interesting, with similar conclusions to what I remember from Mythbusters; that lids reduce the total number of particles found, but that the particles produced from lid use last longer and are larger. So a lid closed situation can;t really be said to be more hygienic.
Unfortunately on a cursory skimming of the other articles none of them seem compare toilets with lid down to lid up, they all seem to look at lidless toilets only. Thus, they can;t really speak to the topic of lid use being more hygienic without the direct comparison.
Mythbusters found it makes virtually no difference, and lid down can actually make particles go further due to the pressure forcing them through a smaller gap.
3D modelling and printing. You do need access to a printer (some libraries have them), but the plastics and resins are cheap, and you can make lots of cool stuff.
Of course, and much of it is on the app store now (which I rarely use myself), but for someone like OPs mom who just wants an easy app store, well there is one.